Table to contain quantiles at a single PERCENTQUANTILE or pointer of tables for several PERCENTQUANTILEs

SEQUANTILES = tables or pointers

Saves standard errors of quantiles

VCQUANTILES = tables or pointers

Saves variance-covariance matrix of quantiles

LQUANTILES = tables or pointers

Saves lower confidence limits of quantiles

UQUANTILES = tables or pointers

Saves upper confidence limits of quantiles

LTOTALS = tables

Saves lower confidence limits of totals

UTOTALS = tables

Saves upper confidence limits of totals

LMEANS = tables

Saves lower confidence limits of means

UMEANS = tables

Saves upper confidence limits of means

LRATIOS = tables

Saves lower confidence limits of ratios

URATIOS = tables

Saves upper confidence limits of ratios

CELLINFLUENCE = variates

Saves influence statistics for individual cells

Description

SVTABULATE procedure calculates estimates from surveys, together with the correct asymptotic standard errors, allowing for the design of the survey. In particular, information about the numbers of sampling units in the survey population is needed and this can be supplied in one of three ways.

1. The WEIGHTS option can be used to supply weights which will generally be the inverse of the probability of selection (pi expansion weights, Sarndal et al. 1992). This is simple, but cannot convey the full design information for multi-stage surveys.

2. The option NUNITS can be used to list the number of primary sampling units per stratum using a table or variate with one value for each stratum. Similarly, in a two-stage design, NSECONDARYUNITS indicates the number of secondary units in each primary sampling unit.

3. The dataset can contain the full survey population with unsampled (or non-responding) units indicated by missing values for the response variables. This allows Genstat to deduce the numbers of units without the need to supply any further information; it is thus simple to use, but is not feasible with large or complex surveys. The NUNITS (and NSECONDARYUNITS if appropriate) option should be set to a value of -1 to indicate that this is required.

Other information on the survey design is provided using the STRATUMFACTOR and SAMPLINGUNITS options.

The response variable is specified using the Y parameter. Estimated counts of the number of observations can be produced by leaving the parameter unset (this is equivalent to analysing a vector of 1’s). The Y parameter can also be left unset if the procedure is used to calculate survey weights. The X parameter can be set in order to produce estimates of the ratio Y/X. By default estimates of totals, means or ratios are for the whole population, but the CLASSIFICATION option can be set to one or more factors defining subsets of the data for which estimates are required. The list of CLASSIFICATION factors can also include pointers defined using the FMFACTORS procedure, representing a multiple response factor. SVTABULATE generates an ordinary factor to classify the dimension of the tables corresponding to each set of multiple responses. You can supply identifiers for these factors (thus allowing them to be accessed outside the procedure), using the MRFACTOR option.

The FITTEDVALUES parameter is used when estimating population totals via a model-assisted approach. Variance estimates are then calculated using the residual deviation about the fitted values. This can be used in conjunction with the SVCALIBRATE procedure to provide estimates following calibration weighting.

Output is controlled by the PRINT and PLOT options. The latter produces various plots that are useful in identifying outliers and influential points which may require further investigation. The setting single of the PLOT option produces a scatterplot of values of Y against X, whilst separate produces a separate graph for each combination of levels of the CLASSIFICATION factors. (excluding multiple response factors). The graphs are log-transformed, unless negative values are present. If the log-transformation is required and zeros are present a small constant is added first. When X is unset, both single and separate produce a scatterplot of Y against CLASSIFACTION. The weights and influence settings produce histograms of the weights and influence statistics respectively. The setting diagnostic produces a scatterplot of influence statistics against weights; this plot tends to be more informative than the histograms with large datasets. The influence statistic for an observation is defined as the absolute percentage change in the total estimate when the observation is replaced by a missing value and the associated weight redistributed to other units in the same stratum. When CLASSIFICATION is set, influence statistics are printed for individual cells in the table of results, as well as for the grand total. When PRINT is set to influence, details are printed of the observations with the highest influence; the number printed can be controlled by the NINFLUENCE option. By default this output is labelled by the row number of the observation, but the LABELS parameter can be used to specify more meaningful identifiers in the form of a variate, text or factor.

The FPCOMIT option is provided so that the finite population correction (see e.g. Sarndal et al. 1992) can be omitted. This is usually done when a simplified variance estimate is produced for multistage samples by ignoring the within-cluster component of variation (the ultimate cluster approach); since this is non-conservative, the omission of the FPC is sometimes advocated to counteract this and to ensure that standard errors are appropriate. Genstat will produce the ultimate cluster results if it is only provided with the survey weights (i.e. NUNITS and NSECONDARYUNITS left unset), but this approach is not recommended since the correct analysis can be produced with little extra effort.

Results of the analysis can be saved using the parameters TOTALS, MEANS, RATIOS and QUANTILES, with the corresponding standard errors using SETOTALS, SEMEANS, SERATIOS and SEQUANTILES. Confidence limits are saved using LTOTALS, LMEANS, LRATIOS and LQUANTILES for the lower limits, and UTOTALS, UMEANS, URATIOS and UQUANTILES for the upper limits. By default, 95% confidence limits are produced, but this may be changed using the CIPROBABILITY option. When the Y parameter is unset, TOTALS, SETOTALS, LTOTALS and UTOTALS contain estimated counts of observations. Numbers of (non-missing) observations and the sum of the weights can be saved using the NOBSERVATIONS and SUMWEIGHTS parameters. These are set to tables classified by the CLASSIFICATION factors; if CLASSIFICATION is unset, they are they are set to a table with a single cell labelled 'All data'. The OUTWEIGHTS and INFLUENCE parameters allow you to save variates containing the weights and influences, respectively. CELLINFLUENCE saves the influence statistics with respect to the individual cells in the table of results, as opposed to the influence statistics for the grand total, which is saved by the INFLUENCE parameter. The WALD parameter can be used to save Wald statistics comparing means between the different levels of the CLASSIFICATION factors.

The simplest quantile, and the one produced by default, is the median (50% quantile), but the PERCENTQUANTILE option allows you to request any percentage point between 1 and 99. Moreover, by specifying a variate as the setting for PERCENTQUANTILE, you can obtain several quantiles at the same time. However, if you then want to save the results, the setting of the QUANTILES parameter must be a pointer with length equal to the required number of quantiles, instead of a single table.

By default, standard errors and confidence limits are based on Taylor-series approximations. However, bootstrap standard errors can be obtained by setting the NBOOT option to the desired number of bootstrap samples. For exploratory analyses a relatively low value (perhaps 20) may suffice, but where test statistics or confidence limits are required a value of at least 400 is recommended. The CIMETHOD option controls how the confidence limits are formed:

percentile

uses simple percentiles of the bootstrapped distribution;

tdistribution

calculates a standard error from the bootstrapped estimates and then uses the t-distribution to form intervals;

logit

is for proportions, and ensures that the calculated limits lie between 0 and 1 (see Heeringa et al. 2010);

automatic

uses the percentile method when at least 400 bootstrap samples have been used, otherwise it uses the t-distribution method when Y is set, and the logit method when Y is not set.

The default is CIMETHOD=automatic.

The bootstrapping method is selected using the METHOD option. In a one-stage design the default of simple forms each bootstrap sample by sampling with replacement from the original sample within each stratum. In a two-stage design (i.e. if SAMPLINGUNITS is set), primary sampling units are first sampled with replacement, and then secondary units are sampled with replacement within the selected primary units. Variance estimates from the boostrapping process will be biased where there are very few sampling units in each stratum and so the method is not recommended in this situation. The setting METHOD=sarndal constructs a “pseudo-population” by replicating each sampled unit by the rounded value of its weight, so that, for example, an observation with weight 16.1 is represented sixteen times in the pseudo-population (see Sarndal et al. 1992, page 442). The bootstrap sample is formed by sampling with replacement from this pseudo-population. Option SEED provides a seed for the random sampling.

Method

The procedure uses the methods for survey analysis described in most survey analysis textbooks; Sarndal et al. (1992) give the best account of these for the case where weights vary within a stratum or sampling unit. If the dataset contains the full population, as opposed to just sampled or responding units, the options NUNITS and/or NSECONDARYUNITS can be set to -1, in which case the procedure calculates the numbers using TABULATE.

When bootstrapping is used, bootstrap samples are formed using the SVBOOT procedure.

Restrictions of the Y variate or any of the CLASSIFICATION factors are used to define a subpopulation, and the estimates produced relate to that subpopulation. Any restrictions on SAMPLINGUNITS, STRATUMFACTOR or WEIGHTS are ignored.